The document discusses rounding decimals and estimating sums, differences, products, and quotients. It provides methods like front-end estimating and clustering to improve accuracy in estimates. Examples and practice problems are included to reinforce these estimation techniques.

1. Rounding And Estimating Section 3.1 By Ms. D-H

2. Rounding Decimals You can round decimal numbers when you don’t need exact values. Review: 38. 4 1 0 .7772 7,098. 5 6 274.94 3 4 5. 0 25 9.8 5 1 Tenth, 38.4 Ones, 1 Tenths, 7,098.8 Thousandths, 274.943 Tenths, 5.0 Hundredths, 9.85

3. Estimating Sums and Differences You can estimate an answer before you calculate, to make sure your answer is reasonable. The symbol  means “is approximately equal to.” One way to estimate is to round all of the numbers to the same place value.

4. Estimating with Decimals Estimate to find whether each answer is reasonable. +130  +125.73 590  590.63 460  464.90 Estimate Calculation

5. Try This: Estimate 355.302 + 204.889 = 453.56 – 230.07 = About 560 About 220

6. Front-End Estimating Gets you closer to the exact sum than estimating by rounding. Add the front-end digits. (to the left of the decimal) Round to estimate the sum of the remaining digits (to the right of the decimal) Combine the two estimates. (add)

7. Front-End Estimating Use Front-End Estimating: $ 1 .10 $ 1 .73 $ 2 .71 $ 4 . .10 .73 .71 . ? Estimate by Rounding. .10 .70 .70 1.50 Now add, $4 + $1.50 = $5.50 The total cost is about $5.50.

8. Try This: Estimating using Front-End Estimation. 6.75 + 2.2 + 9.58 = about… $1.04 + $2.49 + $7.40 = about…

9. Clustering Use clustering to estimate the sum of several numbers that are close to one value. Example: Phone Bills for 4 Months What dollar amount do the 4 bills cluster around? $15.00 is our cluster value. 4 bills at,  $15 means 4 • $15 = $60 is  the total cost. August: $15.05 July: $14.90 June: $16.05 May: $15.35

10. Try This: Using Cluster Estimating $4.50 + $5.20 + $5.55 = 26.7 + 26.2 + 24.52 + 25.25 + 23.9 = About $15 About 125

11. Estimating Decimal Products and Quotients Section 3.2

12. Estimating Products You can use MENTAL MATH to estimate a product. This is a good way to check your work! Estimate! 7.65 • 3.2 = ? 7.65 (by rounding) = 8 3.2 (by rounding) = 3 8 • 3  24 7.65 • 3.2  24

13. Try This: Estimating Products 4.72 • 1.8  17.02 • 3.78  8.25 • 19.8 

14. Word Problem!!! Arlene bought 6 yards of fabric. The fabric cost $6.75/yard. The sales clerk charged Arlene $45.90 before tax. Did the clerk make a mistake? Explain. $6.75  $7 $7 • 6 yards = $42 Rounded to the nearest dollar. Multiplied the estimate. The sales clerk made a mistake. Since $6.75 < $7, the actual cost should be less than the estimate. The clerk should have charged Arlene less than $42.00 before tax.

15. Try This: Word Problem You buy 8 rolls of film for your camera (cause it is ancient). Each roll costs $4.79. Estimate the cost of the film before tax. $4.79 is rounded to $5 $5 • 8 rolls = $40 $4.79 • 8  $40.00 Eight rolls of film at this price is about $40.00 total.

16. Estimating Quotients: Things to Remember Dividend Divisor Quotient Compatible Numbers : numbers that are easy to divide mentally. 24  8 = 3

17. Estimating Quotients Round the divisor. Round the dividend to a compatible number. 38.9  1.79  11.95  2.1  82.52  4.25  1.79  2, 38.9  39, so 39  2 19 2.1  2, 11.95  12, so 12  2 6

18. Assignment #15 Practice 3.1: Rounding and Estimating (All) Practice 3.2: Estimating Decimal Products and Quotients (All) 50 problems total.